The fact that you saw the doctor a week after the incident shouldn't be a problem. Submit all medical records, invoices and documentation relating to your injury. If you do not receive a satisfactory response from the store, you still might be able to locate an attorney who accepts small cases. Alternatively, you can file a small claims suit and handle the matter yourself.
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Send a demand letter along with copies of the medical records to the store's insurer. Ask for out of pocket costs, medical bills paid by your insurer, and pain and suffering. You can find a sample demand letter online to use as a template.
Keep in mind that you insurer will want subrogation if you get any money out of the store. That means, you'll need to pay them back for any medical expenses paid by them, to some extent.
Finally, the store will likely not pay you what you feel you deserve. If they admit liability, you'll probably be offered your medical bills and maybe some meager amount for your pain and suffering to make you go away. I suggest you find an attorney who doesn't only take on million dollar cases. There are plenty of attorneys who would agree to help you. If you want to maximize your damages, I suggest you find one.
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Mr. Lee and Leydicker are correct. A one week gap in treatment is not uncommon or unreasonable. Document all aspects of your damages and you just might be able to resolve things directly. If you feel the offer (if any) is unreasonable you should be able to find someone to help negotiate on your behalf.
Get the police report or store report if there is one, witness statements if any, medical bills and records including anything you paid out of pocket plus what insurance paid. Send this to the insurance company with a demand. I do agree that this sounds like a small claims case.